1. Field of the Invention
The present invention relates to monolithic nonplanar ring oscillators (NPROs). More specifically, the present invention relates to designating the optimal geometry for a monolithic NPRO given the index of refraction and Verdet constant of a designated medium. Even more specifically, the present invention relates to optimal geometries for monolithic NPROs in materials having index of refraction greater than approximately 1.47.
2. Summary of the Prior Art
The prior art has presented the advantages of end-pumped monolithic nonplanar ring oscillators (NPROs). In general, monolithic nonplanar ring oscillators can operate as unidirectional, single-frequency lasers in the presence of a sufficiently strong magnetic field. End-pumping of the monolithic NPRO provides an efficient means of exciting only the TEM.sub.00 mode of the laser, and end-pumping greatly reduces the thermal load on the laser. End-pumping with diode laser sources is particularly efficient. A monolithic laser has a rugged, mechanically stable resonator. Unidirectional oscillation in a ring laser overcomes the problem of spatial hole burning and allows the laser to operate in a single longitudinal mode, even at high output powers. Unidirectional operation of a ring laser also leads to improved resistance to optical feedback. An end-pumped, unidirectional, monolithic NPRO is thus an efficient source of narrow linewidth laser radiation with improved immunity to the deleterious effects of back-reflected radiation.
All devices of the prior art have used Nd:YAG or Nd:GGG as the laser medium. It is desirable to extend the concept of the monolithic NPRO to other media, especially laser glasses. There are several strong motivations for doing so, including improved injection locking of highpower pulsed glass laser systems, the engineering of laser resonators with extremely low quantum linewidth limits, and the potential of developing monolithic resonators with small thermo-optic coefficients. Any glass-based system requiring a narrow linewidth stable oscillator would benefit from the development of a monolithic NPRO in laser glass.
There are also considerable practical advantages to using laser glass for making monolithic NPROs. First, the optical quality of laser glass can be superior to that of most crystalline materials. Second, the cost of high quality laser glass is small compared to that of high quality laser crystals. Third, specialized manufacturing techniques have been developed for use with glass which cannot usually be applied to crystalline media. These practical and physical considerations make the development of a design for monolithic NPROs constructed from media of widely varying indices of refraction extremely important.
U.S. Pat. No. 4,578,793, issued Mar. 25, 1986 to Kane and Byer, entitled Solid-State Non-Planar Internally Reflecting Ring Laser, describes the requirements for unidirectional oscillation in a monolithic nonplanar ring oscillator. The fundamental requirement is an adequate loss difference between the two possible directions of propagation around the ring. The laser will operate unidirectional in the direction of lower loss when the loss difference is sufficiently large. To produce a difference between the round trip losses of the two directions of propagation requires an optical diode. The three essential elements required to form an optical diode are: 1) a reciprocal (propagation-direction-independent) polarization effect, 2) a nonreciprocal (propagation-direction-dependent) polarization effect, and 3) a partial polarizer.
Discrete-element Faraday effect optical diodes have long been used to enforce stable unidirectional operation of solid-state, He-Ne, and ring dye lasers. The optical diode creates a polarization-dependent difference in loss for the eigenmodes of the two directions of propagation around a ring. The loss difference is produced by a combination of a reciprocal polarization rotator such as c-axis quartz, a nonreciprocal rotator such as a Faraday rotator, and a polarizer. Ideally, one arranges the reciprocal and nonreciprocal rotations to cancel for one direction of propagation and to add for the other. In the direction in which the rotations cancel, the eigenpolarizations are the low and high loss linear polarization states aligned with the principal axes of the partial polarizer. For the direction in which the rotations add, the eigenpolarizations are in general linear or elliptical polarization states with losses intermediate between the maximum and minimum possible values. An optical diode having these properties is said to be optimal.
Kane and Byer describe a means of producing an optical diode in a monolithic nonplanar ring oscillator. The elements of the optical diode are as follows. The reciprocal polarization-influencing effect is provided by a nonplanar ring light path defined by three total internal reflections (TIRs) and one reflection from a multilayer dielectric-coated output coupler. The nonreciprocal effect is provided by Faraday rotation in the laser medium when the laser resonator is immersed in an applied magnetic field. Oblique reflection from the output coupler implies that the p (in-plane) and s (perpendicular) reflection coefficients for the output coupler are different, so the output coupler functions as a partial polarizer.
Referring to FIGS. 1a-b, a schematic of the nonplanar ring light path for a prior art four-reflection NPRO 10 is shown. The light path is the perimeter of a three-dimensional geometric figure formed by joining two isosceles triangles (ABD and BCD) along a common base (BD). The dihedral angle between the two planes of the triangles is denoted by .beta. (FIG. 1b). For any value of .beta. other than 0 or 180 degrees, the light path is nonplanar. The light path has a plane of reflection symmetry (ACE). A uniform magnetic field B is applied parallel to AE.
The preferred embodiment of Kane and Byer involved a nonplanar ring light path in Nd:YAG in which the two planes of propagation (planes ABD and BCD in FIG. 1) of the light meet at right angles (.beta.=90 degrees). Trutna et al., in U.S. Pat. No. 4,747,111 for a Quasi-Planar Monolithic Unidirectional Ring Laser has shown that a significant advantage accrues from a change in the geometry of the light path. In the preferred embodiment of Trutna et al. the two planes of propagation of the light in Nd:YAG meet at an angle of .beta.=1.25 degrees instead of 90 degrees. The advantage of this geometry is that the associated optical diode is more closely analogous to the ideal discrete-element optical diode described previously. The loss associated with the low-loss direction of propagation is made as small as is permitted by the choice of the output coupler 12. Moreover, the loss difference between the two directions of propagation for similar-sized NPROs in the presence of a given applied magnetic field is much larger for the quasi-planar case than for the right-angle case. In other words, the quasi-planar design permits unidirectional oscillation induced by a much smaller magnetic field than for the right-angle geometry.
As noted earlier, prior art devices have used high-index-of-refraction, crystalline laser materials such as Nd:YAG (n=1.82) or Nd:GGG (n=1.94) as the medium for their monolithic resonator. All devices of the prior art have used four-reflection nonplanar ring light paths comprising three TIRs and a single reflection from the output coupler. Some of the relative advantages of different geometries for the nonplanar ring light path have been considered. It has been shown that significant advantages accrue to devices in which the combination of the geometry of the light path and the applied magnetic field lead to an optical diode that best emulates the ideal discrete-element optical diode in producing a low loss for the oscillating direction and a high loss for the non-oscillating direction.
The prior art descriptions of diode-laser-pumped monolithic glass lasers have, additionally, envisioned four-reflection monolithic Nd:Glass NPRO with a right-angle light path geometry. It is illustrated by implication of the analysis herein that such an NPRO cannot operate optimally as envisioned. Moreover, it has been experimentally shown that four-reflection, monolithic Nd:glass NPROs fail to run unidirectionally, even using large magnetic fields. These experimental results underscore the importance of paying careful attention to the optical diode properties of the monolithic NPRO.